Average square speed in Maxwell—Boltzmann statistics¶
For an ideal gas, the average square of speed is directly proportional to its temperature and inversely proportional to the mass of the gas.
Notation:
\(k_\text{B}\) (
k_B
) isboltzmann_constant
.
Conditions:
The gas is in thermal equilibrium with the environment.
The gas particles are distributed according to Maxwell—Boltzmann statistics.
Links:
- Symbol:
avg(v^2)
- Latex:
\(\langle v^{2} \rangle\)
- Dimension:
velocity**2
- equilibrium_temperature¶
Equilibrium
temperature
of the gas.
- Symbol:
T
- Latex:
\(T\)
- Dimension:
temperature
- Symbol:
m
- Latex:
\(m\)
- Dimension:
mass
- law¶
avg(v^2) = 3 * k_B * T / m
- Latex:
- \[\langle v^{2} \rangle = \frac{3 k_\text{B} T}{m}\]